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Annual Meeting Optical Society of America

Two-frequency above threshold ionization with pulses

L. Wang, J. W. Haus, K. Rzazewski

Published Jan 1, 1989• 0 citations
Publisher

Abstract

We solve a model with one bound state and two continua.1 Two lasers are used to study the above threshold ionization process. The first laser couples the electron in a bound state to a continuum state. The photons are assumed to be energetic enough to promote the electron directly into the continuum far from the threshold; this avoids complications due to the Rydberg levels and the ponderomotive shifts of the threshold. The second laser mixes the electron wavefunction between two continuum states (C—C transitions); since we avoid the rotating wave approximation, multiple transitions between these continua are allowed. We find that the ionization rate is unaffected by the C—C transitions. Our model of hydrogenic atoms allows redistribution among the continua only during the ionization process and the photoelectron spectra exhibits peak suppression; i.e., the population is not the strongest at the energy of the ionization laser.

DOI
10.1364/oam.1989.fb3

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We solve a model with one bound state and two continua.1 Two lasers are used to study the above threshold ionization process. The first laser couples the electron in a bound state to a continuum state. The photons are assumed to be energetic enough to promote the electron directly into the continuum far from the threshold; this avoids complications due to the Rydberg levels and the ponderomotive shifts of the threshold. The second laser mixes the electron wavefunction between two continuum states (C—C transitions); since we avoid the rotating wave approximation, multiple transitions between these continua are allowed. We find that the ionization rate is unaffected by the C—C transitions. Our model of hydrogenic atoms allows redistribution among the continua only during the ionization process and the photoelectron spectra exhibits peak suppression; i.e., the population is not the strongest at the energy of the ionization laser.
A model of atomic ionization by smooth pulses is solved with bound-continuum and energy-dependent continuum-continuum (C-C) dipole coupling. The rotating-wave approximation for the C-C transitions is avoided. In contrast with the flat continuum result, our ionization rate is independent of the C-C coupling. We also derive the photoelectron energy spectra and show that counterrotating terms make important contributions. Relation to above-threshold ionization experiments with two frequencies is discussed.
The dynamics of the bound-state populations and the photoelectron spectra are calculated for model atomic systems irradiated by a pulse with a harmonically modulated frequency. For a system including a single bound state a model is adopted, which takes into account the threshold behavior typical of negative ions and admits continuum-continuum transitions. For a model one-dimensional atom the results are obtained through a numerical integration of the Schr\"odinger equation. The case of a resonant ionization is also considered. The modulation of the frequency results in changing the instantaneous rate of decay of the initial state, in inducing additional population oscillations for multilevel systems, and in additional peaks in the photoelectron spectra.
We consider the excitation of atomic hydrogen in its ground state by an intense radiation field tuned close to the ionization threshold. Results are presented for the ac Stark shift of the 1s and 2s states, the width of the 1s state, and the photoelectron energy spectrum. In the first instance, our nonperturbative approach includes the 1s state, the p series of excited states, and the p continuum: we demonstrate that the p Rydberg states generate a rich structure in the photoelectron energy spectrum through the action of the counter-rotating wave dynamics when the laser frequency is tuned below the ionization threshold. We then go on to analyze in detail how the interaction of the p states with the other Rydberg series and continua increases the width of the p states; it is shown, however, that at the field intensities considered here (\ensuremath{\approxeq}1013{10}^{13}1013 W ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}2}$), this effect is not sufficient to smear out the structure in the photoelectron energy spectrum.
We present a discussion of the two-color above-threshold ionization process, performed with the aim of studying strong-field continuum–continuum transitions. We extend the approach of Rzażewski [ J. Opt. Soc. Am. B7, 481 ( 1990)] to obtain analytically solvable equations for the multiple continuum model analyzed by Deng Eberly [ J. Opt. Soc. Am. B2, 486 ( 1985)]. Some comments on the effect of continuum–continuum transitions on the line shape of a laser-induced continuum structure are also made.
Continuum–continuum, bound–bound, bound–free, and free–bound atomic field-induced transitions are investigated. The initial atomic state is supposed to be given by a wave packet of coherently populated levels of continuous or discrete spectra. Interference effects were found to increase the probabilities of these types of transition and to change their dependence on the pulse duration τ. Interference is shown to occur also in the two-photon ionization probability with highly excited Rydberg levels as intermediate states. Criteria of applicability of the energy diffusion model are formulated. The different diffusion criteria are shown to be incompatible with each other, owing particularly to described interference effects. An alternative picture of multiphoton excitation is suggested. This picture is similar to the above-threshold ionization and predicts the appearance of some maxima in the spectrum of excited electrons below the ionization threshold.